Two classic examples are mathematical expressions and a language with the "if then else" construct with optional "else".

The expression 1+1+1 can parse as (1+1)+1 or 1+(1+1). The expression "if X then if Y then A else B" can parse two different ways. The "else" can either belong to the internal "if" or the external "if". With parens, the parses are "if X then (if Y then A else B)" and "if X then (if Y then A) else B".

What do you mean ambiguous rules? Context free languages have rules that can form an ambiguous language but the rules aren't ambiguous...My PLT prof always liked to point out that all natural languages are ambiguous....actually "all" might be a little strong but it's certainly safe to say most and obviously English is.